Courbes elliptiques sur un anneau et applications cryptographiques

Abstract : The goal of this thesis is to study cryptographic applications of elliptic curves over the ring Fp["], with Fp a finite field of prime order p and with the relation "2 = 0. In a first time, we describe these curves defined over a ring. Then, we study the algorithmic properties by proposing eective implementations for representing the elements and the group law. Finally, we study some of their cryptographic properties, with the description of : an attack of the elliptic discrete logarithm problem (over a finite field) using these curves ; a cryptosystem à la ElGamal over these curves. We study its security properties
Document type :
Theses
Complete list of metadatas

Cited literature [60 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00401449
Contributor : Jean-Louis Thomin <>
Submitted on : Friday, July 3, 2009 - 10:49:27 AM
Last modification on : Friday, January 12, 2018 - 1:50:59 AM
Long-term archiving on : Tuesday, June 15, 2010 - 7:21:34 PM

Identifiers

  • HAL Id : tel-00401449, version 1

Collections

Citation

Marie Virat. Courbes elliptiques sur un anneau et applications cryptographiques. Mathématiques [math]. Université Nice Sophia Antipolis, 2009. Français. ⟨tel-00401449⟩

Share

Metrics

Record views

451

Files downloads

2132